Existence result for a free-discontinuity energy governing the detection of spots in image processing

Analysis of a New Variational Model to Restore Point-Like and Curve-Like Singularities in Imaging

“…Hence, from a variational point of view, we have to nd a functional space whose elements are able to produce Radon measures, whose support contains the singularities we would like to preserve. Then, in line with recent works for detecting point-like target problem (see [5,14,15]), we consider the divergence as an operator able of producing Radon measures concentrated on points and curves. We deal with the space ∆M p loc (Ω) of W 1,p loc -functions whose gradient is an L p -vector eld with distributional divergence given by a Radon measure, where…”